Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in PYTHON3):

Solution:
'''input
7
'''
# its just a simulation
from sys import stdin, setrecursionlimit
import heapq


def create_matrix(m):
	matrix = [[0 for x in range(m)] for y in range(m)]
	return matrix



def check(num):
	if num * 2 - 1  >= n:
		return True
	else:
		return False

def print_matrix(m, matrix):
	count = 0
	x = 0; y = 1
	flag = True
	while True:
		if count == n:
			break
		if flag:
			x += 1
			print(x, y)
			flag = False
			count += 1
		else:
			y += 1
			print(x, y)
			flag = True
			count += 1

# main starts
n = int(stdin.readline().strip())
start = 1
end = 1000
matrix = create_matrix(250)
while True:
	#print(start, end)
	if start >= end:
		if check(start - 1):
			start -= 1
		
		break


	mid = (start + end) // 2
	if check(mid):
		end = mid - 1
	else:
		start = mid + 1

if check(start):
	print(start)
	print_matrix(start, matrix)
else:
	check(start + 1)
	print(start + 1)	
	print_matrix(start + 1, matrix)